We study a non-cooperative two-sided facility location game in which facilities and clients behave strategically. This is in contrast to many other facility location games in which clients simply visit their closest facility. Facility agents select a location on a graph to open a facility to attract as much purchasing power as possible, while client agents choose which facilities to patronize by strategically distributing their purchasing power in order to minimize their total waiting time. Here, the waiting time of a facility depends on its received total purchasing power. We show that our client stage is an atomic splittable congestion game, which implies existence, uniqueness and efficient computation of a client equilibrium. Therefore, facility agents can efficiently predict client behavior and make strategic decisions accordingly. Despite that, we prove that subgame perfect equilibria do not exist in all instances of this game and that their existence is NP-hard to decide. On the positive side, we provide a simple and efficient algorithm to compute 3-approximate subgame perfect equilibria.

翻译：我们研究了一种不合作的双向设施定位游戏,设施和客户在其中表现策略性。这与许多其他设施定位游戏不同,客户只是访问最近的设施。设施代理商在图表上选择一个位置,打开一个设施以吸引尽可能多的购买力,而客户代理商则选择哪些设施通过战略分配其购买力来支持其购买力,以最大限度地减少其全部等待时间。在这里,设施的等待时间取决于其所得到的全部购买力。我们显示,我们的客户阶段是一个原子分裂性堵塞游戏,这意味着客户平衡的存在、独特性和高效计算。因此,设施代理商可以有效地预测客户行为并据此作出战略决定。尽管我们证明,在这场游戏的所有情况下,子游戏都不存在完美的平衡,而且它们的存在是难以决定的。在积极的一面,我们提供了一种简单有效的算法,可以计算出三维近端的子游戏的完美平衡。